June is generally the time when summer is at its peak in the North & West and monsoons might start to kick in the the eastern regions. South for sure would be the best place to visit- Wayanard, Ooty, Coorg, Conoor, Allepey are the places that you could shortlist.
If you love beaches then go Bali, Langkawi, Maldives, Phuket...
If you love hill stations, then go to Manali, Dharamshala, Dalhousie, Mcleodganj, Shimla, Nainital, kasol, Kasauli, Kashmir, Shillong, Darjeeling...!